[WIP] loosen nse constraint only after max subcycle is reached

[zhichen3]

PR summary

PR motivation

PR checklist

• [ ] test suite needs to be run on this PR
• [ ] this PR will change answers in the test suite to more than roundoff level
• [ ] all newly-added functions have docstrings as per the coding conventions
• [ ] the CHANGES file has been updated, if appropriate
• [ ] if appropriate, this change is described in the docs

[zingale]

do we still want to consider this?

[zhichen3]

I think its a reasonable thing to do if we were to use these loosen-constraint parameters. But right now I tend to not use them because I think it would make the constraint "too loose".